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arXiv · 2005.12605

Inverse Function Theorem in Fr\'echet Spaces

Milen Ivanov·Nadia Zlateva
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Abstract

We consider the classical Inverse Function Theorem of Nash and Moser from the angle of some recent development by Ekeland and the authors. Geometrisation of tame estimates coupled with certain ideas coming from Variational Analysis when applied to a directionally differentiable function, produce very general surjectivity result and, if injectivity can be ensured, Inverse Function Theorem with the expected Lipschitz-like continuity of the inverse. We also present a brief application to differential equations.

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Milen Ivanov, Nadia Zlateva. 2020-05-26. Inverse Function Theorem in Fr\'echet Spaces. https://doi.org/10.1007/s10957-021-01885-0

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